Consider the points A(2, 4, 6), B(−2, −4, −2), C(4, 6, 4), and D(8, 14, 12). Which of the following statements is/are correct?
1. The points are the vertices of a rectangle ABCD.
2. The mid-point of A C is the same as that of BD.
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Consider the equation of a sphere x2 + y2 + z2 − 4x − 6y − 8z − 16 = 0.
Which of the following statements is/are correct ?
1. z-axis is tangent to the sphere.
2. The centre of the sphere lies on the plane x + y + z − 9 = 0.
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Consider the following statements :
1. The direction ratios of y-axis can be <0, 4, 0>
2. The direction ratios of a line perpendicular to z-axis can be <5, 6, 0>
Which of the statements given above is/are correct?